One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number of sterile males that mate with fertile females but produce no offspring. If $P$ represents the number of female insects in a population, $S$ the number of sterile males introduced each generation, and $r$ the population's natural growth rate, then the female population is related to time $t$ by $$t = \int {\frac{P+S}{P[(r-1)P-S]}}\, dP.$$ Suppose an insect population with 10,000 females grows at a rate of $r$ = 0.10 and 900 sterile males are added. Evaluate the integral to give an equation relating the female population to time.

Note: The resulting equation cannot be solved explicitly for $P$, so your final answer should have the form $t =$ ...

$t =$